Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively.

Answer 1

the nth term of a G S is given by
a1 r^(n-1) where a1 = first term and r = common difference

Answer 2

so the second term = a1 r and 5th term = a1 r^4

so we have

a1 r^4 2301
---- = ----
a1 r -36

Answer 3

Can you find the value of r?

Answer 4

Basically correct. Might be clearer to draw the formula for arith. sequence, or to use Equation to make it fancy-clear.\[a _{n=}a _{0}*r ^{(n-1)}\]

Answer 5

a sub 0 is the first value of the sequence.
r is the common factor.

Answer 6

When you come back online, please let the rest of us know what further info you may need to get started.

Answer 7

i got it guys

Answer 8

thank you

Answer 9

i have another question

Answer 10

Find the sum of the arithmetic sequence.

-4, -1, 2, 5, 8, 11, 14

how do you do that?

Answer 11

There's a simple formula for that.

If s is the sum of the sequence, a is the first term, n is the number of terms, and d is the difference between terms,

s = a + (n - 1)*d

Answer 12

You've typed in a sequence. What are the values of a, n and d here?

Answer 13

um

Answer 14

-4, 7, and i dont know the last one

Answer 15

How far apart are -4 and -1? How far apart are 5 and 8? This should tell you the value of "d."

Answer 16

three

Answer 17

Right. So, a=-4, n=7 and d=3. Can you now find the sum of these 7 terms?

Answer 18

You could check your result by actually adding them up.

Answer 19

waitso i just plug it in

Answer 20

i got 14 ??????

Answer 21

nvmgot it, 35 right

Answer 22

35 is correct